close eclipsing binary bdand: a triple system

Contrib. Astron. Obs. Skalnate Pleso 50, 649 – 671, (2020)https://doi.org/10.31577/caosp.2020.50.3.649

Close eclipsing binary BD And: a triple system

T. Pribulla1,2,3, L’. Hambalek1, E. Guenther4, R. Komzık1,E. Kundra1, J. Nedoroscık4, V. Perdelwitz5 and M. Vanko1

1 Astronomical Institute of the Slovak Academy of Sciences059 60 Tatranska Lomnica, The Slovak Republic, (E-mail: [email protected])

2 ELTE, Gothard Astrophysical Observatory, 9700 Szombathely,Szent Imre h. u. 112, Hungary

3 MTA-ELTE Exoplanet Research Group, 9700 Szombathely,Szent Imre h. u. 112, Hungary

4 Thuringer Landessternwarte, Sternwarte 5, 077 78 Tautenburg, Germany5 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany

Received: October 21, 2019; Accepted: January 8, 2020

Abstract. BD And is a fairly bright (V = 10.8), active and close (P ∼ 0.9258days) eclipsing binary. The cyclic variability of the apparent orbital periodas well as third light in the light curves indicate the presence of an addi-tional late-type component. The principal aim is the spectroscopic testing ofthe third-body hypothesis and determination of absolute stellar parametersfor both components of the eclipsing binary. First medium and high-resolutionspectroscopy of the system was obtained. The broadening-function techniqueappropriate for heavily-broadened spectra of close binaries was used. The ra-dial velocities were determined fitting the Gaussian functions and rotationalprofiles to the broadening functions. A limited amount of photometric datahas also been obtained. Although the photometric observations were focusedon the obtaining the timing information, a cursory light-curve analysis wasalso performed. Extracted broadening functions clearly show the presence of athird, slowly-rotating component. Its radial velocity is within error of the sys-temic velocity of the eclipsing pair, strongly supporting the physical bond. Theobserved systemic radial-velocity and third-component changes do not supportthe 9 year orbit found from the timing variability. Masses of the components ofthe eclipsing pair are determined with about 0.5% precision. Further character-ization of the system would require long-term photometric and spectroscopicmonitoring.

Key words: Stars: individual: BD And; Stars: binaries: eclipsing; Methods:observational; Techniques: spectroscopy

1. Introduction

Gravitational perturbations of a primordial wide binary by a third body causeso called Kozai-Lidov cycles (Kozai, 1962). Cyclic variations of eccentricity ofthe inner binary and changes of the mutual inclination can occur if the mutual

650 T. Pribulla et al.

inclination, j, of the inner and outer orbital planes is 39< j < 141. Duringthe resulting close approaches of the inner binary components in the eccentricorbit tidal friction reduces orbital energy, bringing them closer. If this processis the only evolutionary channel to produce close binary stars, all close binariesmust be accompanied by a third body. Unfortunately, the observational evidenceis strongly biased by techniques used to detect often faint third components.While Pribulla & Rucinski (2006), who used several techniques and numerousobservations, found at least 2/3 of contact binaries to reside in triple or multiplesystems, Rappaport et al. (2013), who searched for eclipse timing variations(light-time effect, LiTE) in the Kepler data, found only about 20% of eclipsingbinaries to be members of triple systems.

The eclipse-timing technique is sensitive to third components on long-periodorbits (see e.g. Pribulla et al., 2012) but it gives only an indication becauseother effects can produce similar variability, e.g. mass transfer or magnetic-orbital momentum coupling (Applegate, 1992). Much more conclusive is thespectroscopic (Pribulla et al., 2006) or visual (Tokovinin et al., 2010) detection.There is, however, still some low probability that the additional component isphysically unrelated. In the case of a wide third-body orbit, the systemic radialvelocity (RV) of the binary should be close to the RV of the third component.For tighter systems mutual orbital revolution is the ultimate proof (Pribullaet al., 2008). An analysis of eclipses in triple systems can sometimes lead notonly to confirmation of multiplicity, but to accurate determination of orbitaland component parameters (see e.g. Carter et al., 2011).

BD And (GSC 3635-1320) is a close (P ∼ 0.9258 days), and relatively bright(Vmax = 10.8) eclipsing binary. It was discovered by Parenago (1938) and sub-sequently analyzed by Florja (1938), who classified BD And as an Algol-typeeclipsing binary with orbital period 0.462899 days and 0.46 and 0.09 mag deepminima. BD And was identified as a ROSAT source by Shaw et al. (1996), andit was detected by Swift (Evans et al., 2013) and twice in the course of theXMM-Newton Slew Survey (XMM-SSC, 2018), indicating that the source hasa high level of magnetic activity. Only recently, Sipahi & Dal (2014) obtainedCCD BV R photometry of the system and found that (i) the true orbital pe-riod is two times longer than determined previously, (ii) the mass ratio of theeclipsing binary is about 0.97, (iii) minima times show a cyclic variability indi-cating presence of a third body on about 9.6-year orbit, and (iv) light variationoutside the primary eclipse may result from γ Dor oscillations of the primarycomponent. Subsequently Kim et al. (2014) analyzed extensive new BV R pho-tometry as well as published timing data. The data analysis confirmed periodicorbital period variations indicating a third component revolving on a highlyeccentric orbit with e ∼ 0.76. The light-curve (LC) variability was interpretedby dark photospheric spots on the hotter component. An LC analysis showedabout 14% third-light contribution. None of the above observations showed anyflares in spite of the strong spot activity indicated by a large and variable LCasymmetry.

Close eclipsing binary BD And: a triple system 651

Unfortunately, no spectroscopic observations have been published yet, leav-ing the question of the system’s multiplicity open. Therefore, we observedBD And spectroscopically from 2016 to 2019 and obtained additional BV IcCCD photometry.

The layout of the paper is as follows. In Section 2, we briefly describe newspectroscopic and photometric observations. In Section 3, we present the anal-ysis of the spectroscopy. The timing variability is presented in Section 4 whileLC and broadening-function (hereafter BF) modeling in Section 5. Third-bodyparameters and orbit are discussed in Section 6. The surface activity of the closebinary in Section 7. The paper is concluded in Section 8.

2. New observations and data reduction

2.1. Echelle spectroscopy

Medium and high-dispersion spectroscopy of BD And was obtained with threespectrographs. At Stara Lesna observatory the observations were performed atthe G1 pavilion with a 60cm, f/12.5 Zeiss Cassegrain telescope equipped with afiber-fed echelle spectrograph eShel (see Thizy & Cochard, 2011; Pribulla et al.,2015). The spectrograph has a 4150-7600 A (24 echelle orders), spectral rangeand a maximum resolving power of about R = 11,000. The ThAr calibration unitprovides about 100 m s−1 RV accuracy. An Atik 460EX CCD camera, which hasa 2749×2199 array chip, 4.54 µm square pixels, read-out noise of 5.1 e− and gain0.26e−/ADU, was used as the detector. The observations were also performedwith a 1.3m, f/8.36, Nasmyth-Cassegrain telescope equipped with a fiber-fedechelle spectrograph at Skalnate Pleso. Its layout follows the MUSICOS design(see Baudrand & Bohm, 1992). The spectra were recorded by an Andor iKon-LDZ936N-BV CCD camera, with a 2048×2048 array, 13.5µm square pixels, 2.9e−

read-out noise and gain close to unity. The spectral range of the instrument is4250-7375A (56 echelle orders) with the maximum resolution of R = 38,000.Additional spectra were obtained at Thuringer Landessternwarte Tautenburgwith the Alfred Jensch 2m telescope and coude echelle spectrograph. Thesespectra cover 4510-7610 A in 51 orders. A 2.2′′ slit was used for all observationsgiving R = 31,500. The journal of observations is in Appendix A.

Because of the short orbital period of BD And of P∼0.9258 days, the expo-sure times were limited to 900 seconds (about 1.1% of the orbital period) toprevent orbital-motion smearing.

The raw data obtained with the 60cm and 1.3m telescopes were reduced usingIRAF package tasks, Linux shell scripts and FORTRAN programs as describedin Pribulla et al. (2015). In the first step, master dark frames were produced.In the second step, the photometric calibration of the frames was done usingdark and flat-field frames. Bad pixels were cleaned using a bad-pixel mask, cos-mic hits were removed using the program of Pych (2004). Order positions weredefined by fitting Chebyshev polynomials to tungsten-lamp and blue LED spec-


Table 1. Journal of photometric observations of BD And. The table lists evening date(yyyymmdd), orbital phase range, No. of points, photometric filter, estimated scatter,time of the minimum light, and the instrument used. The instruments are: G1 - SBIGCCD camera in G1 pavilion at Stara Lesna and G2 - FLI CCD camera in G2 pavilionat Stara Lesna. The phases were computed using the same ephemeris as in Table 5.

Date Phases No. Filter σ HJDmin Inst.2 400 000+

20170809 0.890 - 1.000 217 B 0.0034 – G220170809 0.890 - 1.000 214 I 0.0033 – G220170810 0.025 - 0.081 111 B 0.0042 – G220170810 0.023 - 0.081 116 I 0.0046 – G220170815 0.171 - 0.484 560 B 0.0029 – G220170815 0.171 - 0.484 524 I 0.0031 – G220171107 0.758 - 1.130 502 B 0.0032 58065.40493(13) G220171107 0.757 - 1.131 504 V 0.0040 58065.40581(8) G220171115 0.494 - 0.604 134 V 0.0038 – G120171116 0.537 - 0.548 14 V 0.0049 – G120171124 0.139 - 0.214 88 V 0.0045 – G120180720 0.454 - 0.580 208 B 0.0036 58320.46604(4) G220180720 0.455 - 0.580 204 I 0.0044 58320.46593(8) G220180724 0.752 - 0.951 314 B 0.0031 – G220180724 0.752 - 0.951 307 I 0.0038 – G220180803 0.471 - 0.767 471 B 0.0027 58334.35305(6) G220180803 0.471 - 0.768 471 I 0.0032 58334.35279(16) G220180804 0.547 - 0.621 117 B 0.0030 – G220180804 0.548 - 0.620 116 I 0.0037 – G220180807 0.841 - 0.094 394 B 0.0029 58338.51898(4) G220180807 0.842 - 0.094 397 I 0.0032 58338.51901(4) G220180909 0.000 - 0.000 226 B 0.0027 58371.38370(6) G220180909 0.000 - 0.000 219 I 0.0036 58371.38393(4) G220180921 0.000 - 0.000 317 B 0.0025 58383.41891(13) G220180921 0.000 - 0.000 299 I 0.0035 58383.41915(10) G220181123 0.000 - 0.000 350 B 0.0026 58446.37438(6) G220181123 0.000 - 0.000 353 I 0.0034 58446.37445(7) G2

tra. In the following step, scattered light was modeled and subtracted. Aperturespectra were then extracted for both the object and the ThAr lamp and thenthe resulting 2D spectra were dispersion solved. The spectra obtained at TLSwere reduced under the IRAF environment (see Hatzes et al., 2005; Guentheret al., 2009; Hartmann et al., 2010).

2.2. CCD photometry

A limited amount of BV I photometric data was obtained. Its primary goal wasto better define the ephemeris for the spectroscopic observations. The data wereobtained at the Stara Lesna observatory with a 18cm f/10 auxiliary Maksutov-Cassegrain telescope attached to the Zeiss 60cm Cassegrain used to obtain theechelle spectroscopy (G1 pavilion). An SBIG ST10 XME CCD camera and theJohnson-Cousins filters were used. The field of view (FoV) of the CCD camera


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Figure 1. Broadening functions of BD And extracted from the MUSICOS spectrasorted in phase (left) and ordered by date (right). The red horizontal line denotesthe average radial velocity of the third component. The vertical dashed black linesseparate individual observing seasons.

is 28.5×18.9′. Additional photometry was obtained with another 60cm ZeissCassegrain telescope (G2 pavilion) using a Fingerlakes ML 3041 with a back-illuminated CCD (FoV is 14.1×14.1′). The filter set is also close to the Johnson-Cousins system.

The CCD frames were photometrically reduced under the IRAF environ-ment. First, master dark and flat-field frames were produced, then bad pixelswere cleaned and the frames were photometrically calibrated. Prior to aperturephotometry all frames were astrometrically solved to define the pixel to WCS1

transformation. To minimize the effects of the second-order extinction, 7 nearbystars (No. 9, 11, 12, 15, 16, 19, and 20 following designation in Table 1 of Kimet al., 2014) with the total effective color (B − V ) = 0.586, close to that ofBD And were chosen as comparison stars. For the largest airmass during ourobservations, X = 1.68, the effect of the second-order extinction in the V pass-band is <0.003 mag. For both telescopes the same set of comparison stars wasused. A journal of the photometric observations is given in Table 1.

The heliocentric minima times determined by the Kwee & van Woerden(1956) method are listed in Table 1. The minima times are affected by the LCasymmetry, which is most marked in the B passband. For example, the egressfrom the minimum is considerably steeper on November 7, 2017, so the minimumof light occurs slightly earlier than the spectroscopic conjunction. LC was muchmore symmetric in 2018.

3. Broadening functions and radial velocities

Spectra of BD And were analyzed using the BF technique developed by Rucinski(1992). The BFs have been extracted in the 4900-5510 A spectral range (freeof hydrogen Balmer lines and telluric lines) for all three spectrographs. The

1World Coordinate System


velocity step in the extracted BFs was set according to the spectral resolution.For eShel at G1 the step of ∆RV = 5.8 km s−1 was used, for the MUSICOS andcoude echelle spectrograph at TLS, ∆RV = 3.5 km s−1.

BFs were extracted using HD65583 (G8V) as the template. The extractedBFs clearly show three components: two rapidly-rotating components of theeclipsing pair and a slowly rotating third component (Fig. 1). The third com-ponent shows practically constant RV.

The BFs were first modeled by triple Gaussian functions. The model Gaus-sian profile corresponding to the third component was then subtracted from BFs.The BFs showing non-blended components were fitted by a double rotationalprofile (see Pribulla et al., 2015). The resulting RVs of the binary componentsare given in Appendix A. The rotational velocities of the components measuredoutside eclipses are v1 sin i1 = 69.0±0.7 km s−1, v2 sin i2 = 68.8±1.2 km s−1 forMUSICOS at SP, and v1 sin i1 = 70.8±1.2 km s−1, v2 sin i2 = 70.7±0.8 km s−1

for coude echelle at TLS. The projected rotational velocity of the third compo-nent is below the spectral resolution, thus v3 sin i3 ≤ 8 km s−1. The slow rotationrate is a natural consequence of the magnetic breaking in a single late-type star.

The BFs extracted from the TLS and SP spectra are significantly less noisyand result in more precise RVs than those extracted from the G1 spectra. TheRV of the third component derived from the SP and TLS spectroscopy is about−10.3 km s−1. BFs from G1 clearly show the third component, but its profileis too noisy to determine the RV reliably.

Our spectroscopic observations resulted in 112 RVs for all three components.Because the time range of the observations is only about 3 years, the orbitalperiod of the eclipsing pair was adopted from equation (2) of Kim et al. (2014). Acircular orbit was assumed with the longitude of the periastron passage ω = π/2.RVs of the primary and secondary component were modeled simultaneously.Errors of the RVs were estimated from equation (1) of Hatzes et al. (2010).Assuming the same rotational velocity and spectral range, we have:

σRV ∝1

SNR R3/2, (1)

where SNR is the signal-to-noise ratio and R is the spectral resolution. Havinga sufficient number of spectra for every spectrograph, the RV errors were firstderived from the signal-to-noise ratios as 1/SNR. The errors were then re-scaledto give the reduced χr = 1 for every spectrograph.

The scaling factors for eShel at G1 are 92 and 91 for the primary and sec-ondary component, respectively. The scaling factors for MUSICOS at SP are37 and 36 for the primary and secondary component, respectively. The scalingfactors for coude echelle at TLS are 33 and 74 for the primary and secondarycomponent, respectively. After re-scaling the errors, all RVs were modeled si-multaneously. The resulting best parameters are given in Table 2 and the cor-responding fits are plotted in Fig. 2.


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Figure 2. RV measurements of the primary, secondary and tertiary components ofBD And and the corresponding Keplerian orbit fits. The point sizes scale with theirweights (1/σ2).

Using the inclination angle, i = 92.72 ± 0.19, from Table 7 of Kim et al.(2014), one gets M1 = 1.135±0.006 M and M2 = 1.140±0.004 M. While themass of the primary component is close to the estimate of Kim et al. (2014),the secondary is about 13% more massive and the components are of equalmass within the margins of error. Our inclination angle i = 86.48 ± 0.04 (seeSection 5) gives the masses only by about 0.5% larger than the minimum massesprovided by the spectroscopic orbits.

4. Timing variability and light-time effect

BD And shows periodic variability of the orbital period, indicating the presenceof a third component in the system. Although the cyclic variability is clearlyvisible (see Fig. 3), the minima times are affected by the LC asymmetries result-ing from dark photospheric spots. Moreover, the minima times were determinedby different methods and obtained in different filters. Because the componentsare covered with cold spots (Kim et al., 2014), the spot effects are increasing inmagnitude towards violet.

The observed-computed (O-C) diagram of Kim et al. (2014) shows that theolder photographic and visual minima timings are unusable because of the large


Table 2. Spectroscopic elements of the primary and secondary components of BD And.The best fit is based on 112 RV measurements (30 from eShel, 50 from MUSICOS,and 32 from TLS).

Parameter Value σP [d] 0.92580526 –T0 [HJD] 2 457 931.1648 0.0003V0 [km s−1] −11.11 0.13K1 [km s−1] 143.75 0.17K2 [km s−1] 143.24 0.29q =M2/M1 1.0035 0.0024a1 sin i [R] 2.629 0.003a2 sin i [R] 2.620 0.005M1 sin3 i [M] 1.132 0.005M2 sin3 i [M] 1.136 0.004

scatter. Hence, we used CCD minima times only. In addition to the minimalist of Kim et al. (2014) and our new observations, minima times were collectedfrom publications of Parimucha et al. (2016), Hubscher (2015, 2017), Samolyk(2015a,b, 2018a,b, 2019a,b). Because of unsure and missing errors, two datasetswere analyzed: (a) CCD minima with available error estimates (149 times), and(b) all CCD minima timings assuming the same errors/weights (164 times). Inthe latter case the error for all minima has been set to 0.0001 days. The observedminima times were modeled assuming a LiTE and a continuous period change:

Min I = Tmin + P × E +Q× E2 +

+a12 sin i12

c

[1− e2

12

1 + e12 cos ν12sin(ν12 + ω12) + e12 sinω12

],

where Tmin + P × E + Q × E2 is the quadratic ephemeris of the eclipsingpair, a12 sin i12, e12, ω12, ν12 is the projected semi-major axis, the eccentricity,the longitude of periastron passage, and the true anomaly of the eclipsing-pairorbit around the common center of gravity, respectively. The data optimizationwas done assuming the linear ephemeris (Q = 0, i.e., a constant period) andquadratic ephemeris (a continuous period change with dP/dt = const) of theeclipsing pair.

The resulting reduced χ2r for a continuous-period change are 31.1 and 71.1

for the first (a) and the second dataset (b), respectively. Very high χ2r indicates

that the published errors are underestimated or/and there is an additional in-trinsic variability present in the timing data. To get reduced χ2

r ∼ 1 the meanobservation error must be about 0.0008 days. The resulting parameters for bothdatasets are given in Table 3. The corresponding fit (all CCD minima, datasetb) together with predicted and observe systemic-velocity changes is shown inFig. 3.


Table 3. The light-time orbit of the eclipsing pair around the common center ofgravity with the third component. Reduced χ2

r is given. For dataset (b) σ = 0.0008days was assumed for every datapoint. The time of the periastron passage, T12, andthe time of the minimum light, Tmin, are given without 2 400 000. The mass of thethird component M3 is given for i3 = 90 (minimum mass).

Parameter Dataset (a) Dataset (a) Dataset (b) Dataset (b)quadratic linear quadratic linear

Tmin [HJD] 34 962.846(9) 34 962.8696(9) 34 962.851(5) 34 962.8677(8)P [day] 0.9258070(8) 0.92580489(4) 0.9258065(5) 0.92580496(3)Q [day] −4.7(17) 10−11 – −3.7(11) 10−11 –P3 [day] 3299(37) 3259(31) 3358(26) 3324(18)e12 0.64(9) 0.58(7) 0.74(12) 0.70(10)ω12 [deg] 296(7) 295(7) 308(6) 308(5)T12 [HJD] 49 450(80) 49 510(80) 49 430(60) 49 490(40)a12 sin i12 [a.u.] 0.78(6) 0.74(4) 0.86(13) 0.82(9)f(m) [M] 0.0057(13) 0.0051(9) 0.0077(34) 0.0068(21)M3 [M] 0.34(3) 0.33(3) 0.38(8) 0.36(4)χ2r 31.1 32.4 1.111 1.180

d.o.f. 149-8 149-7 164-8 164-7

A hypothesis that the orbital period of the eclipsing pair is constant (Q =0) was tested using the F-test for case (b) where more data are available. Forthe false-rejection probability of α = 0.05 the critical value is F = 3.9, while thecalculated value of the F statistics is 9.6. This means that the quadratic term isstatistically significant. A possible cause for the observed period decrease in theeclipsing pair could be the angular momentum loss due to the magnetic breaking.A very week quadratic term was already found by Kim et al. (2014) from ashorter dataset (6984 vs. 9110 days). On the other hand, older photographicminima times2 require a constant period of the eclipsing pair.

The LC asymmetry effect on the minima times can be estimated using for-mula (6) of Pribulla et al. (2012). Assuming an orbital period of P = 0.9258days and parameters estimated from Fig. 8 of Kim et al. (2014), D ∼ 0.15P(minimum duration), d ∼ 0.4 (eclipse depth), and AOCE ∼ 0.05 mag we get∆t = 0.002 days, which is comparable to the LiTE amplitude (see Fig. 3). Thismeans that the LiTE orbit is rather unreliable and additional information onthe LC asymmetry would be needed to disentangle the spot and LiTE effectsto arrive at useful orbital elements.

5. Broadening-function and light-curve modeling

The LC analysis of BD And is complicated by the surface activity resulting inwave-like distortions. A detailed analysis of BV R photometry of the systemwas performed by Kim et al. (2014). Our photometry is inferior to their databecause it was focused on obtaining the timing information. Another problem

2see e.g., http://var2.astro.cz/ocgate/


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Figure 3. The O-C diagram for all available minima times of BD And (dataset a)with the best light-time effect model. The residuals are plotted for linear ephemerisT0 = HJD 2 434 962.87143+ 0.925804848×E. The blue points correspond to the meanseasonal times of the spectroscopic conjunctions. One-sigma limits are plotted withdashed lines (top). The corresponding RV-change of the eclipsing pair and the thirdcomponent is also shown together with seasonal mean values (bottom). The blue linecorresponds to the mass center of the eclipsing pair and the magenta line to the thirdcomponent.

is that the LC changes on the timescales as short as weeks or months. Theonly dataset obtained within a reasonably short time is the BIc photometryfrom the G2 pavilion from August 3 till September 9, 2018. Unfortunately, theobservations do not cover the maximum following the primary minimum. Ourbest available spectroscopy (TLS data) was obtained from July 27 till August6, 2018, thus partially overlapping with these photometric data. BFs obtainedafter subtraction of the third component from the triple Gaussian model wereused.

The simultaneous modeling of BFs and LCs was done using the code Roche(see Pribulla et al., 2018). The simultaneous analysis is crucial to lift the pa-rameter degeneracies complicating even modeling of high-precision satellite LCs.Such is e.g. the correlation between the component radii and inclination angle(see Southworth et al., 2007).

Possible surface inhomogeneities were ignored due to the large phase gapin our photometric data preventing a sound analysis. The orbital period was


not adjusted but fixed at P = 0.92580526 days (see Kim et al., 2014). Thefollowing parameters are used T0 - time of the periastron passage, P - orbitalperiod, i - inclination angle, Ω1, Ω2 - surface equipotentials, T1 and T2 polartemperatures of the primary and secondary component, l3 - third light, l12 - LCnormalization factor, spectroscopic elements - V0, (K1+K2) and BF backgroundand normalization factors. The limb darkening was modeled using the linearlimb-darkening law and tables of van Hamme (1993). The reflection effect andgravity darkening were computed assuming convective envelopes with β1 = β2

= 0.08, and A1 = A2 = 0.5. The component fluxes were computed using modelatmosphere spectral energy distribution taking into account local gravity andtemperature. The polar temperature of the primary was fixed at 5550 K as foundfrom the infrared color indices (see Section 6). Third light was not adjusted andfixed at l3/(l1 + l2) = 0.1481 in the B passband and l3/(l1 + l2) = 0.1933 in theIc passband corresponding the the results of Kim et al. (2014). A circular orbitand synchronous rotation of the components were assumed.

The BIc LCs and their best fits are shown in Fig. 4. The best parametersare listed in Table 4. The modeling shows that the observations (especially theB data) show systematic deviations very probably caused by the surface in-homogeneities. We also note that the third light is strongly correlated to theinclination angle: the larger the third light the larger the inclination angle.

Obtaining a more reliable parameter set would require long-term monitor-ing of the system. Constructing the brightest LC (see Section 6 of Pribullaet al., 2001) could provide a better reference for the modeling of individualspot-affected LCs.

Table 4. Simultaneous modeling of BIC light curves and broadening functions fromthe TLS spectra assuming all proximity effects using Roche. Luminosity uncertaintieswere computed assuming temperature errors of 100 K.

Roche Kim et al. (2014)Parameter σ σV0 [km s−1] −11.11 0.12 – –K1 +K2 [km s−1] 288.04 0.27 – –q =M2/M1 1.0017 0.0020 0.8770 0.0031T1 [K] 5550 – 5880 –T2 [K] 5522 3 5842 3i [deg] 86.48 0.04 92.72 0.19R1 [R] 1.239 0.004 1.278 0.020R2 [R] 1.243 0.005 1.155 0.018a [R] 5.281 0.004 5.152 0.055M1 [M] 1.152 0.003 1.145 0.053M2 [M] 1.154 0.003 1.001 0.047L1 [L] 1.31 0.09 1.75 0.19L2 [L] 1.29 0.09 1.39 0.15log g1 [cgs] 4.313 0.003 4.284 0.024log g2 [cgs] 4.311 0.004 4.314 0.024


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Figure 4. BI light curves of BD And obtained from August 3 till September 9, 2018and their best fits resulting from the simultaneous modeling of light curves and broad-ening functions.

6. Third component and the outer orbit

The existence of a third component on a long-period orbit was first indicatedby the timing variability and third light in the LC modeling (see Sipahi & Dal,2014). Our new spectroscopy conclusively shows the presence of an additionalcomponent.

The light contribution of the third component, l3/(l1 + l2), determinedfrom the Gaussian-function multi-profile fit is 0.213±0.005 (observations in aneclipsing-binary phase interval from 0.163 to 0.344). This means that the 3rdcomponent is slightly later than the components of the eclipsing binary. The lightcontribution of the components in the spectrum reflects the relative strength ofmetallic lines (mostly Fe I, Fe II, Mg I). Because the 3rd component is of alater spectral type than the eclipsing binary and the metallic-line strength in-creases from G to K spectral types, the determined third light is overestimated.To correct this effect, the dependence of BF strength on (B − V ) for the solarmetallicity from Table 3 of Rucinski et al. (2013) was used. Assuming that thebinary components are of G1V spectral type and the third component is of G7Vtype (Kim et al., 2014, Tables 8 and 10) and that the metallicity of all threestars is the same, the correction factor is 0.838. Thus the third-light contributionis l3/(l1 + l2) = 0.178±0.004 or l3/(l1 + l2 + l3) = 0.151±0.004 in the spectral


range where BFs were extracted (4900-5400A). This is in a good agreement withthe photometrically-determined value l3/(l1 + l2 + l3) = 0.143±0.006 in the Vpassband (Kim et al., 2014).

The observed combined infrared color of BD And is J −K = 0.449±0.026.If we neglect the interstellar reddening (see Kim et al., 2014), this correspondsto a G6-7V spectral type with one sub-type uncertainty or Teff = 5550±100 K(Cox, 2000). If all three stars are main-sequence objects, the observed infraredcolor can be obtained having two components of the G5V spectral type anda late-type companion of the K2V spectral type. Then the combined infraredcolor is J − K = 0.446 and third light is l3/(l1 + l2) = 0.151, which is a bitless than our spectroscopic determination l3/(l1 + l2) = 0.178. Combining twomain-sequence components of G6V spectral type and a K2V main-sequence starresults in l3/(l1 + l2) = 0.171, but with a slightly redder combined color J−K =0.464. The late spectral types of the components indicated by the infrared colorare, however, inconsistent with their masses, if they are main-sequence objects.

The predicted 9-year orbital revolution of the eclipsing pair around the com-mon center of gravity is expected to cause changes of its systemic velocity. Toget some constraint on the outer orbit, the RVs were divided into individual ob-serving seasons. We kept RV semi-amplitudes, K1,K2, of the components fixed,varying only the time of the spectroscopic conjunction, T0, and systemic velocity,V0. Resulting systemic velocities are V0 = −10.63 ± 1.19 km s−1 (2016/2017),V0 = −10.13±0.38 km s−1 (2017/2018), V0 = −11.16±0.13 km s−1 (2018/2019),and V0 = −11.86± 0.43 km s−1 (2019/2020). The average RV of the third com-ponent per season and instrument was also computed3. The resulting RV dataand the timing of the spectroscopic conjunction are plotted in the (O-C) diagramin Fig. 3.

The systemic velocity and RV of the third component were observed to beidentical within about 1-2 km s−1 and so V0 ∼= V3. This practically confirms thegravitational bond of the third component to the eclipsing pair. The observedsystemic RV changes (see Section 3) of the eclipsing pair and the third compo-nent are, however, inconsistent with the LiTE orbit. The predicted RV differencedepends on the mass ratio M3/(M1 + M2). Assuming that M3/(M1 + M2) =0.41 (Kim et al., 2014), the LiTE fit predicts the RV difference to decrease fromV0 − V3 = −1.8 km s−1 to V0 − V3 = −5.5 km s−1 during our spectroscopy,which is not observed. While the third component shows a constant velocity,the systemic velocity of the eclipsing pair seems to be slowly decreasing. Thismeans that (i) the timing variability is caused by the LiTE but the determi-nation of ω12 or/and e12 is incorrect and affected by the LC asymmetries, or(ii) the component causing the timing variability is not visible in the spectra.In the latter case, the body which causes the timing variability and eclipsing

3The only deviating point is the RV obtained from the MUSICOS data in the 2018/2019season when better observations were obtained at TLS. This point was excluded from furtherconsiderations.


0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

6540 6550 6560 6570 6580

No

rma

lize

d f

lux

Wavelength [A]

phase 0.735, Teff=5300 K

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

6540 6550 6560 6570 6580

No

rma

lize

d f

lux

Wavelength [A]

phase = 0.325phase = 0.735

Figure 5. Comparison of the observed Hα line profile (TLS spectrum fromHJD 2 458 336.42400) and the synthetic spectrum for Teff = 5300 K convolved withcorresponding BF at phase φ = 0.735 (right). The bottom plot shows comparisonof two spectra obtained at TLS at φ = 0.325 (HJD 2 458 330.48948) and φ = 0.735(HJD 2 458 336.42400).

binary systemic velocity changes must be an intrinsically faint object unseen inthe spectra.

A more reliable characterization of the third component would require spec-troscopic observations covering the entire long-period orbit. An important re-quirement is the long-term RV stability of the instrument(s) at the level of atleast 100-200 m s−1.

7. Surface activity

BD And is composed of two solar-like components. Unlike our Sun, the compo-nents are fairly fast rotators with projected rotational velocities about 70 km s−1.Thus one can expect enhanced photospheric and chromospheric activity.

The best indicator of the surface activity are chromospheric lines Ca II Hand K, Hα and Ca IRT (see e.g., Eker et al., 1995; Biazzo et al., 2006; Zhanget al., 2015). Our spectroscopic observations cover only Hα. In chromosphericallyactive stars Hα has typically a lower equivalent width (EQW) compared to thatexpected for the given spectral type. To determine the extra emission, syntheticspectra have been calculated using code iSpec (Blanco-Cuaresma et al., 2014a,b)assuming various effective temperatures Teff = 5100, 5300, 5500 and 5700 K, theSolar metallicity, log g = 4.3 [cgs] and the microturbulent velocity ξ = 2 km s−1.The synthetic spectra were then convolved with extracted BFs. The resultingconvolved synthetic spectra for Teff ≤ 5500 K match the depth of the observedHα line profile very well and do not indicate any extra emission (see Fig. 5). Onthe other hand, for two components of the same brightness and temperatureas indicated by the combined LC and BF solution and practically equal masses(Section 3) we see different line depth (Fig. 5, bottom). The EQW is higher for


the primary component. This indicates some surface activity on the secondarycomponent lowering its EQW.

We searched for direct spot signatures in the BFs extracted from the TLShigh-dispersion and high SNR spectroscopy. The third component, representedby a model Gaussian function, was subtracted. The BFs were extracted frommetallic lines not affected by chromospheric activity. To enhance the spots inBFs, their best fits by the Roche-code modeling (see Section 3) were subtracted.The resulting residuals (Fig. 6) do not conclusively show the presence of spots.The analysis of BD And is, however, complicated by the presence the third com-ponent which cannot be completely subtracted. Moreover, the observed profilesof the components do not perfectly follow the theoretical predictions based onthe solid-body rotation.

8. Discussion and conclusions

Extensive echelle spectroscopy conclusively showed that eclipsing binary BD Andis part of a hierarchical triple system. The RVs of all three components weredetermined using the BF technique appropriate for heavily broadened spectraof close binaries. The power of this deconvolution method is documented by thefact that useful RVs were determined even from low SNR spectra obtained witha 60cm telescope.

The eclipsing pair is composed of two almost identical solar-type compo-nents accompanied by a late-type star. Throughout our observations the thirdcomponent showed a constant RV very close to the systemic velocity of thebinary, strongly supporting the gravitational bond. The orbital motion in theouter, 9-year orbit indicated by the timing variability could not be detectedspectroscopically. The difference of the systemic velocity of the eclipsing pairand RV of the third component is inconsistent with the outer orbit based onthe timing information. The minima times are probably shifted from spectro-scopic conjunction by the surface spot activity. This negatively influences thedetermination of the orbital elements. Hence, future photometric observationsshould be obtained in the I passband least affected by the spots but still ac-cessible by silicon-based CCDs. Having both primary and secondary minimaobserved within a couple of days is also important. This would enable one tobetter quantify the spot effects on the timing information.

The identification of the third component seen in the BFs extracted fromvisual spectroscopy with the additional component indicated by the timing vari-ability is spurious. The minimum mass of the third component found from theLiTE modeling ranges from 0.33 to 0.38 M. If it is a main-sequence star on anedge-on orbit, its light contribution would be <1% (see Xia et al., 2008). Thenthe component seen in spectra is another star on a much wider orbit.

The projected semi-major axis of the eclipsing pair around the common cen-ter of gravity found from minima timing is a12 sin i12 = 0.86±0.13 a.u. (case b


0

5

10

15

20

25

-400 -200 0 200 400

Phase b

in

RV [km/s]

-0.1

-0.05

0

0.05

0.1

0.15

Figure 6. Residuals from the BF fitting. Only TLS observations are plotted. TheRV span of both components is indicated by solid black lines. The correspondingorbital-phase ranges (from bottom) are 0.111-0.173 (6 rows), 0.325-0.437 (9 rows) and0.655-0.879 (13 rows). Only spectra from July/August 2018 are shown.

with quadratic ephemeris). The corresponding systemic velocity of the eclipsingpair is predicted to range from −1.8 km s−1 to +5.5 km s−1. Such RV variabilityshould easily be detected even with modest spectrographs. Long-term spectro-scopic observations are crucial to determine the outer-orbit elements and mutualinclination of the inner and outer orbit. Of special importance is the determi-nation of the mass ratio M3/(M1 +M2).

Interferometric observations would be hard to perform because of the lowbrightness of the system (J = 9.504 ± 0.022, H = 9.164 ± 0.021,K = 9.055 ±0.014, 2MASS) even if the expected maximum separation of the eclipsing pairis about 20 mas (see Kim et al., 2014).

The unusable trigonometric parallax from Gaia DR2 (Gaia Collaborationet al., 2018), π = 0.13±0.63 mas is, very probably, resulting from the pertur-bations of an additional component (e.g., variability induced motion). It is,however, possible, that the astrometric motion will be taken into account in thefinal data release. In order to check the distances, we derived X-ray luminositiesfrom the ROSAT catalog by converting count rate and hardness ratio into aphysical flux with the method described by Schmitt et al. (1995). The resultingflux, as well those from the Swift and XMM-Newton observations, were thenconverted into luminosities by assuming the distances in question. For a dis-


tance of 294 pc (Kim et al., 2014), this yields LRASSX = (7.2 ± 1.9) · 1030 erg/s,

LSwiftX = (2.8± 1.1) · 1031 erg/s and LXMM

X = (1.5± 0.5) · 1031 erg/s, which cor-responds to log(LX/Lbol)=−3.3, −2.7 and −2.97, respectively. The resultingX-ray luminosities are in good agreement with each other and indicate that thesystem is highly active at the saturation limit of log(LX/Lbol)=−3. This alsoindicates that a distance larger than ∼ 300 pc is physically implausible, since itwould implicate that all of the components of BD And are above the saturationlimit.

Acknowledgements. The authors thank V. Kollar for his technical assistance.This work has been supported by the VEGA grant of the Slovak Academy of SciencesNo. 2/0031/18, by the Slovak Research and Development Agency under the contractNo. APVV-015-458. This work was also supported by the GINOP 2.3.2-15-2016-00003of the Hungarian National Research, Development and Innovation Office and the Cityof Szombathely under Agreement No. 67.177-21/2016. This research has made useof NASAs Astrophysics Data System and the SIMBAD database, operated at CDS,Strasbourg, France. The authors thank an anonymous referee for his/her constructivecomments.

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A. Radial-velocity observations

Table 5. Journal of spectroscopic observations of BD And. The table gives heliocentricJulian date, barycentric RVs for all three components, signal-to-noise ratio and theinstrument used. The instruments are: G1 - eShel spectrograph in G1 pavilion atStara Lesna, SP - MUSICOS spectrograph at Skalnate Pleso, TLS - Coude echelle atTautenburg. Only observations where radial velocities of all three components couldbe determined are listed. The computer readable form of these data can be found at:https://www.astro.sk/caosp/Eedition/FullTexts/vol50no3/pp649-671.dat/.

HJD RV1 RV2 RV3 SNR Inst.−2 400 000 [km s−1] [km s−1] [km s−1]

57727.17144 103.3 −137.4 −7.9 13 G157727.18283 112.5 −141.4 −8.8 14 G157727.19328 115.6 −140.4 −10.0 15 G157753.16967 141.4 −147.4 −14.7 12 G157753.18048 117.1 −159.5 −12.8 10 G157753.19241 132.9 −153.9 −14.8 13 G157753.20425 124.7 −153.5 −12.7 17 G157754.19736 106.8 −128.0 −6.8 17 G157754.20782 102.0 −118.7 −8.0 17 G157754.22026 95.3 −108.4 −4.0 16 G157754.23120 90.0 −90.8 −6.5 14 G157966.56809 −156.5 119.8 −14.0 14 G157966.57901 −149.7 130.1 −2.9 13 G157968.50619 −146.5 103.6 −4.9 10 G157968.51727 −131.1 111.8 −10.7 10 G157968.52890 −137.8 114.8 −8.3 10 G157987.51260 100.9 −121.2 −10.8 11 G157987.52308 66.5 −108.4 −19.9 10 G157987.53357 93.3 −103.3 −9.0 10 G157991.45162 −115.3 84.6 −13.2 14 G157991.46211 −106.1 98.0 −13.6 13 G157991.47276 −124.8 105.1 −10.1 14 G157991.48326 −130.3 108.2 −9.4 14 G157991.49389 −138.6 112.3 −8.2 13 G157991.50444 −127.1 114.9 −9.0 12 G157992.53812 −149.3 131.2 −12.5 12 G157992.54905 −153.5 127.7 −11.8 12 G158028.46393 −86.2 80.2 −9.6 17 G158073.36486 76.4 −94.5 −8.2 19 G158113.26396 127.6 −148.5 −3.4 11 G158060.52132 131.8 −151.6 −10.4 24 TLS58060.53281 132.5 −152.4 −10.4 29 TLS58060.54355 133.2 −154.8 −10.3 28 TLS58060.55429 133.5 −152.3 −10.2 28 TLS58081.29493 −129.9 107.3 −10.5 12 SP


Table 5. Continued.


58081.30922 −139.9 118.8 −10.1 12 SP58081.32243 −142.6 124.3 −9.7 13 SP58134.17812 −147.8 128.7 −11.7 15 SP58134.19155 −148.7 127.6 −10.1 16 SP58134.20553 −142.8 122.2 −10.0 15 SP58134.21896 −136.1 118.3 −10.2 17 SP58134.23299 −130.6 107.9 −10.3 17 SP58327.51391 −105.4 77.1 −9.9 33 TLS58327.52534 −112.9 85.7 −9.8 35 TLS58327.52599 −112.7 89.4 −12.0 14 SP58327.53668 −119.9 99.0 −9.9 34 TLS58327.53901 −121.6 94.2 −12.1 15 SP58327.54786 −125.4 105.7 −9.8 33 TLS58327.55192 −128.6 107.1 −11.9 16 SP58327.55964 −132.3 111.4 −10.0 33 TLS58327.57104 −139.2 117.3 −10.3 35 TLS58328.51309 −146.8 120.3 −11.3 15 SP58328.54287 −156.1 122.3 −12.5 11 SP58328.55978 −158.1 126.5 −12.0 14 SP58328.57425 −159.0 133.3 −12.1 14 SP58330.48948 −137.5 117.6 −10.4 38 TLS58330.50053 −132.6 110.8 −10.3 39 TLS58330.51137 −127.9 106.1 −10.5 38 TLS58330.52868 −116.3 95.2 −10.6 38 TLS58330.54287 −108.0 84.9 −10.5 39 TLS58331.48629 −95.3 70.2 −10.1 38 TLS58331.49716 −84.2 56.1 −10.0 37 TLS58331.50795 −73.4 49.0 −10.0 32 TLS58331.51879 −63.7 38.3 −10.2 32 TLS58334.49805 109.1 −130.6 −10.2 36 TLS58334.50951 114.2 −136.3 −10.3 36 TLS58334.52045 119.5 −141.3 −10.3 36 TLS58334.53156 122.7 −146.3 −10.6 36 TLS58334.54239 127.1 −148.6 −10.3 36 TLS58336.40274 128.3 −151.3 −9.9 39 TLS58336.42400 132.4 −153.2 −9.8 45 TLS58336.45072 131.3 −152.6 −10.0 44 TLS58336.47203 128.7 −150.4 −9.8 47 TLS58336.49351 123.2 −143.0 −9.9 46 TLS58336.51476 113.3 −134.6 −10.0 44 TLS58336.53603 101.3 −121.9 −10.0 43 TLS58336.55729 88.2 −109.8 −10.0 46 TLS58358.51050 53.9 −100.9 −11.8 13 SP58358.52196 72.3 −102.9 −10.5 13 SP


Table 5. Continued.


58360.49929 128.3 −156.2 −10.6 14 SP58360.51073 129.9 −155.8 −10.5 15 SP58360.52220 135.3 −156.0 −10.4 15 SP58360.54154 129.1 −151.8 −11.5 14 SP58360.55300 122.5 −146.6 −10.8 16 SP58360.56446 121.1 −142.5 −10.6 14 SP58374.49887 89.6 −121.2 −12.2 12 SP58374.51033 88.0 −110.7 −11.4 13 SP58374.52179 80.2 −105.6 −11.1 18 SP58374.53482 70.7 −90.6 −11.2 19 SP58431.30439 −146.9 133.3 −9.9 11 SP58431.31585 −155.3 130.5 −10.3 12 SP58431.32732 −147.3 135.2 −9.7 12 SP58431.34228 −153.1 127.9 −9.9 10 SP58431.35374 −150.8 131.5 −10.6 9 SP58705.43381 −140.9 117.5 −10.0 11 SP58705.44527 −137.6 110.3 −10.4 11 SP58705.45672 −127.6 106.6 −9.7 11 SP58721.52721 125.2 -149.1 −10.4 15 SP58721.53866 127.7 -151.5 −10.2 15 SP58721.55013 131.1 -153.5 −10.7 15 SP58723.52282 97.3 -120.7 −10.4 13 SP58723.53427 89.8 -113.0 −10.3 13 SP58781.38578 -119.9 100.4 −10.5 17 SP58781.39911 -116.7 89.1 −10.5 17 SP58781.41057 -106.1 82.7 −10.1 17 SP58795.31985 -89.0 67.8 −9.8 10 SP58811.25235 90.3 -110.1 −10.8 10 SP58811.26380 92.8 -122.4 −10.5 13 SP58811.27524 102.8 -122.0 −10.3 13 SP58823.25516 61.4 -85.3 −10.8 15 SP58823.26662 70.9 -98.0 −10.2 15 SP

close eclipsing binary bdand: a triple system

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